Prepare For Point Exam

Introduction 

                    In geometry, topology and related branches of mathematics a spatial point describes a specific object within a given space that consists of neither volume, area, length nor any other higher dimensional analogue. Thus, a point is a 0-dimensional object. The following figure shows a finite set of points in two dimensional.

                                                         two dimensional graph               

  Now we shall solve some example problems regarding prepare for point exam.                                                                                                                                                

 

Example problems to prepare point exam:

 

                   In the point exam, the point related problems like how to find slope, how to find distance between the points can be asked. A example problems related to point are given below which will help you for the exam. These problems help you to prepare for the point exam.

Example 1:

Find the distance between the points (7, 5) and (3, 10).

Solution:

      Step 1: Assign variables

                                               x1 = 7     x2 =3

                                               y1= 5    y2 = 10                            

     Step 2: Use the distance formula

                                              d = ((x2 - x1)2 + (y2 - y1)2)

     Step 3: Plug all values in the distance formula

                                                =  √(((3 - 7)2 +  (10 - 5)2)

     Step 4: Solve the above equation and find distance

                                                =  √((-4) + (5)2)

                                                =  √(16 + 25)

                                                =   √41             

     Step 5: Solution

                             The distance between the given point is 6.403

 

Example 2:

Plot the point (-2, 3) and find out in which quadrant the point (-2, 3) lies?

Solution:

         The given point is (-2, 3). Here, the x coordinate is -2 and y coordinate is 3. If the x-coordinate is negative and y-coordinate is positive, then the point will be in ii quadrant.

                              So, the given point (-2, 3) lies in ii quadrant. In the below graph, the point A shows the given point.

                                a point on coordinate plane                        

Example 3:

Find the slope between the points (6, 9) and (10, 14).

Solution:

    Step 1: Assign the variables                         

                                            x1 = 6     x2 =10

                                            y1= 9    y2 = 14

    Step 2: Slope formula

                                          Slope, m =  `(y_2 - y_1)/(x_2 - x_1)`

    Step 3: Substitute the values in the slope formula and find m

                                                   m = `(14 - 9)/(10 - 6)`

                                                       = `5 / 4`

                                                       = 1.25

     Step 4: Solution

                              The slope of the given point is 1.25

 

Practice problems to prepare for point exam:

 

                                   The following problems help you to prepare for the point exam.

Problem 1: Find the slope between the points (7, 6) and (10, 11).

Problem 2: Find the distance between the points (8, 4) and (9, 18).

Problem 3: Find out in which quadrant the point (-4, -3) lies?

Solutions:

1) 1.67

2) 14.03

3) The given point lies in iii quadrant.